While deep learning has witnessed remarkable achievements in a wide range of applications, its substantial computational cost imposes limitations on application scenarios of neural networks. To alleviate this problem, low-rank compression is proposed as a class of efficient and hardware-friendly network compression methods, which reduce computation by replacing large matrices in neural networks with products of two small ones. In this paper, we implement low-rank networks by inserting a sufficiently narrow linear layer without bias between each of two adjacent nonlinear layers. We prove that low-rank Swish networks with a fixed depth are capable of approximating any function from the Hölder ball $\mathcal{C}^{\beta, R}([0,1]^d)$ within an arbitrarily small error where $\beta$ is the smooth parameter and $R$ is the radius. Our proposed constructive approximation ensures that the width of linear hidden layers required for approximation is no more than one-third of the width of nonlinear layers, which implies that the computational cost can be decreased by at least one-third compared with a network with the same depth and width of nonlinear layers but without narrow linear hidden layers. Our theoretical finding can offer a theoretical basis for low-rank compression from the perspective of universal approximation theory.

Significance testing aims to determine whether a proposition about the population distribution is the truth or not given observations. However, traditional significance testing often needs to derive the distribution of the testing statistic, failing to deal with complex nonlinear relationships. In this paper, we propose to conduct Full Bayesian Significance Testing for neural networks, called nFBST, to overcome the limitation in relationship characterization of traditional approaches. A Bayesian neural network is utilized to fit the nonlinear and multi-dimensional relationships with small errors and avoid hard theoretical derivation by computing the evidence value. Besides, nFBST can test not only global significance but also local and instance-wise significance, which previous testing methods don't focus on. Moreover, nFBST is a general framework that can be extended based on the measures selected, such as Grad-nFBST, LRP-nFBST, DeepLIFT-nFBST, LIME-nFBST. A range of experiments on both simulated and real data are conducted to show the advantages of our method.

Web information extraction (WIE) is a fundamental problem in web document understanding, with a significant impact on various applications. Visual information plays a crucial role in WIE tasks as the nodes containing relevant information are often visually distinct, such as being in a larger font size or having a brighter color, from the other nodes. However, rendering visual information of a web page can be computationally expensive. Previous works have mainly focused on the Document Object Model (DOM) tree, which lacks visual information. To efficiently exploit visual information, we propose leveraging the render tree, which combines the DOM tree and Cascading Style Sheets Object Model (CSSOM) tree, and contains not only content and layout information but also rich visual information at a little additional acquisition cost compared to the DOM tree. In this paper, we present WIERT, a method that effectively utilizes the render tree of a web page based on a pretrained language model. We evaluate WIERT on the Klarna product page dataset, a manually labeled dataset of renderable e-commerce web pages, demonstrating its effectiveness and robustness.